Calculation of exchange constants in spinel ferrites with magnetic S-state ions

The exchange constants in spinel ferrites with S-state ions, including magnesium ferrite, lithium ferrite, and manganese ferrite, were calculated using modified Becke’s three-parameter density functional, where the percentage of Hartree–Fock exchange in total exchange was introduced as a variable parameter (w) to match the experimental results of exchange constants by controlling the localization and delocalization of the electrons. Consistently, the scaling factor of the 3d orbitals of ferric ions was also introduced as a variable parameter (α). From the calculation, the values of parameters w and α matching the experimental results of JAB (nearest-neighbor exchange constant between tetrahedral and octahedral sublattices) were concentrative, while those matching the experimental results of JAA (nearest-neighbor exchange constant inside tetrahedral sublattice) and JBB (nearest-neighbor exchange constant inside octahedral sublattice) were dispersive. Observing that JAB is dominant in most practical ferrima...